It’s probably worth making sure that port is unblocked as that would ultimately be an issue here even if I’m misunderstanding the network situation. Certainly feel free to post your output from a failed connection attempt here to see if it yields any hints.
This is a different product, but we use their same USB Serial connection script and the consensus on their end seems to be that if the PC running the script can access the internet via proxy, then the Arduino connected to that PC via the USB script should be able to use the PC’s network connection as well without further configuration.
If your IT is being slow about responding, you could test this for yourself, see this post where I show how to use PuTTY on a Windows laptop to check to see if it can connect to arduino.mydevices.com on port 8442.